Note the difference of priestly and family communion, all depending on Aaron in verses 9, 10 and 11-13.
Note too, that the first three verses of Lev. 2 are the ordinary meat-offering, from verse 4 the baked meat-offering—the latter dry, or mingled with oil, was for all the males of the family—the baked ones entirely the priest's that offered it; one was isolated offering in Christ alone, the other was general Church communion.
Note, in passing, the wave-breast was for Aaron and his sons; the heave-shoulder for the offering priest. This, however, would seem to be only in the case of the peace-offerings; the trespass-offerings and sin-offerings were for the males only, the heave- and wave-offerings for all the family, see also Leviticus 10:1414And the wave breast and heave shoulder shall ye eat in a clean place; thou, and thy sons, and thy daughters with thee: for they be thy due, and thy sons' due, which are given out of the sacrifices of peace offerings of the children of Israel. (Leviticus 10:14). However, in heave-offerings there seem to be more decided consecration, not for service as presented merely but entirely given up; the Levites were a wave-offering. The heave-offering was an offering of gift, save the heave-shoulder; the heave-offering of dough, Num. 15:19-2119Then it shall be, that, when ye eat of the bread of the land, ye shall offer up an heave offering unto the Lord. 20Ye shall offer up a cake of the first of your dough for an heave offering: as ye do the heave offering of the threshingfloor, so shall ye heave it. 21Of the first of your dough ye shall give unto the Lord an heave offering in your generations. (Numbers 15:19‑21). Lev. 7:1414And of it he shall offer one out of the whole oblation for an heave offering unto the Lord, and it shall be the priest's that sprinkleth the blood of the peace offerings. (Leviticus 7:14), I apprehend, must be one of the unleavened cakes.
The wave-offering seems rather presented to the Lord, and then to subsist for whatever service or use; the heave-offering to have been more offered to the Lord. It is a common word for everything offered to God and given up, so to speak, to Him.